%I A117098
%S A117098 1,4,6,8,9,10,12,14,15,16,20,21,22,24,25,26,27,30,32,33,34,35,36,38,39,
%T A117098 42,44,45,46,48,49,50,51,52,54,55,56,57,58,62,63,64,65,66,68,69,70,74,
%U A117098 75,76,77,80,81,84,85,86,87,88,90,91,92,93,94,95,98,99,100
%N A117098 Numbers n such that nextprime(5*n)<5*nextprime(n) (if p is prime then 
               nextprime(p)=p).
%C A117098 denote f(x)=nextprime(x) let A(p)={n/f(p*n)<f(p)*f(n)} and A(q)={n/f(q*n)<f(q)*f(n)} 
               (q,p are prime) if q<p all terms of A(q) are in A(p). if B(p)={n/
               f(p*n)>f(p)*f(n)} I conjuctured that when p --> infinity, A(p) = 
               All composite positive integers when p --> infinity, B(p) = All primes 
               numbers
%e A117098 nextprime(5*4)=23 and nextprime(5)*nextprime(4)=5*5=25 then 4 is member 
               because 23<15
%o A117098 (PARI) for(i=1,100,if(nextprime(5*i)<nextprime(5)*nextprime(i),print1(i,
               ",")))
%Y A117098 Sequence in context: A046355 A163122 A050655 this_sequence A077136 A098216 
               A063806
%Y A117098 Adjacent sequences: A117095 A117096 A117097 this_sequence A117099 A117100 
               A117101
%K A117098 easy,nonn
%O A117098 1,2
%A A117098 Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Apr 18 2006